Ian Paisley has been described as "stupid" for joining Van Morrison in chatting that Robin Swann is "dangerous" at the Europa Hotel.
Glyn Hanna, an Independent councillor on Newry, Mourne and Down District Council who last week left the DUP alongside colleague, Kathryn Owen, claiming there had been a purge of Jeffrey Donaldson's supporters, said Mr Paisley "should have known better".
"He should not have done that," he told the Irish News.
"I think Robin Swann has done a reasonably good job and even saying that, about Robin Swann is dangerous, is stupid. He can't excuse himself from what he has done".
Kathryn Owen, who is now also an Independent councillor, described Mr Paisley's actions as "unfortunate and unhelpful behaviour".
Ms Owen, who returned to nursing during the pandemic to lend her support, added: "I think Minister Swann has done a very good job under difficult circumstances and hope Mr Paisley reflects on his actions".
Representatives of the main political parties were united in their criticism of Paisley and Morrison, who were likened to "spoiled toddlers stamping their feet".
SDLP leader Colum Eastwood branded the performance as "embarrassing" and "pathetic".
"Those comments fly in the face of those who have died and lost loved ones as a result of Covid-19," he said.
"Van Morrison has let himself down, but Ian Paisley Jr should know better".
Alliance Party leader Naomi Long said both men owned Mr Swann an apology.
"Considering what the entire community has been through in the past year, with many losing loved ones and livelihoods, both Van Morrison and Ian Paisley looked like spoiled toddlers stamping their feet," he said.
"They both owe Robin Swann an apology, and unlike the last leader, the new DUP leadership needs to step up to set some standards and keep Ian Paisley in line".
Sinn Féin assembly member Colm Gildernew said the actions of Mr Morrison and Mr Paisley was "very concerning".
"This sends out a very dangerous public health message at a time when Covid continues to pose a real threat in our communities.
"The DUP need to clarify if Ian Paisley's behaviour reflects the party's view".
Ulster Unionist leader Doug Beattie said he was "absolutely disgusted" by what he saw in the video.
"They should be ashamed of themselves," he said.
"Two grown men who should know better, engaging in a very personal attack on Northern Ireland`s Health Minister".
